Beyond, I found your post very interesting. A definite management predictament. I don't think your "Type A" personality is the whole story here. This situation would be a problem no matter what your personality type.

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they said that I shouldn't have to do the events either because it wasn't right for the head office to ask at short notice for ANYONE to do it--even after I said (again) that it didn't matter what they asked for, only that we had to do it. My job is VERY important to me, and I take it quite seriously

</div></font></blockquote><font class="post">I find it a bit obnoxious that you say your job is very important to you and you take it seriously, as if it isn't important to your co-workers and as if they don't take it seriously. They may be put off by this judgemental attitude. Their jobs may be just as important to them as yours is to you. Don't make assumptions. I can see it would be difficult to get buy in from your co-workers if you broadcast this attitude. I also agree with your co-workers that the short notice from the head office is not working.

I think the situation calls for a face-to-face meeting between your supervisor, your co-workers, and you. One question I have is, are you and your co-workers equal? Or do you supervise them? It seems from your post that you have more responsibility than they do to see that these events get covered. Is that true? But on the other hand you refer to them as "co-workers," as if you are all equals.

At the meeting, you take the lead, "I called this meeting because..." State the facts: the head office gives us very short notice to cover events outside our working hours and we are not always able to fulfill them. How can we deal with this situation? Then ask everyone to brainstorm, and write everyone's ideas up on the board. No idea is too wacky or unreasonable. Just get everyone to stop holding back and throw out their ideas. Don't stop and discuss each idea as it comes up and why it will never work. This makes people stop offering ideas. Just put all the ideas up. When the ideas have stopped, start going through the list and considering the ideas. Maybe you will need to cross some off your list. Maybe others will occur to you as you do this. Maybe a combination of several ideas will be workable. Some ideas that came to my mind were:
--require the head office to give you more notice on when your presence is required at events (2 weeks?, 1 month?)
--borrow staff from other departments to help you when the unexpected arises. Repay them later by helping them out somehow
--hire temporary staff to help with the events. Charge this to the vendor
--hire more staff in your group
--have your supervisor help with the events. this would provide one more body
--ask that the notification of the events go to you and your co-workers simultaneously, if you are not their supervisor. It seems like you are being singled out from the head office to be the enforcer, and that isn't fair to you, unless it indeed is a duty that has been assigned to you.
--let co-workers know that from now on, they will not have to justify the reason why they cannot appear at an event. It is not fair to ask people about their personal lives (I have to go to a wedding, I have to go to my son's game, etc.). This leads to judgments and resentments ("why do they not have to go to the event? I don't have kids and I always have to go, I don't attend church, so I always get stuck with this, etc.) Everyone's reason is equally valid, either they can do it or they can't.
--Perhaps make a minimum commitment required that everyone buys into, such as everyone will have to do at least 2 events per week (provided the agreed upon sufficient notice is provided by the head office).

The trick is to make everyone part of the solution. Don't take this on as your problem alone to solve. You sound like you are at an equal level to your co-workers. This is everyone's problem. Your supervisor really should be taking a stronger role in problem solving, but since she isn't, take the bull by the horns, and do it yourself. Hold the meeting, brainstorm solutions, and come up with something that EVERYONE agrees on.

It could be that you will need to have more players attend your meeting than just your co-workers and your supervisor. Perhaps someone from head office will have to conference in. Or a representative from the vendor (whoever you have the contract with). You know best who should be there.

This is a separate issue from the thing with your car. Don't get sidetracked. Focus on solving the "short staffed for mandatory events" problem.

Also, if it is agreed that you will all talk together with the supervisor, do not shortcut that and talk to her yourself. This will make your co-workers feel betrayed and even less apt to want to serve at events or work together to come up with a solution. Be inclusive. Empower people to be solve this. Your supervisor will be impressed with the way you handle this.

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I don't have any friends outside of my husband. In my closet, I have very little "non-work" clothing. Work is my life.

</div></font></blockquote><font class="post">Are you dissatisfied with this? If so, set some goals to change it. To make some friends, to join in some recreational activities, to not work so much. If this means changing jobs, or transferring to another group within your agency, then start working toward that.